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Simplifying (5a + -2b)(3c + -6d) = 0 Multiply (5a + -2b) * (3c + -6d) (5a * (3c + -6d) + -2b * (3c + -6d)) = 0 ((3c * 5a + -6d * 5a) + -2b * (3c + -6d)) = 0 ((15ac + -30ad) + -2b * (3c + -6d)) = 0 (15ac + -30ad + (3c * -2b + -6d * -2b)) = 0 (15ac + -30ad + (-6bc + 12bd)) = 0 (15ac + -30ad + -6bc + 12bd) = 0 Solving 15ac + -30ad + -6bc + 12bd = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '6bc' to each side of the equation. 15ac + -30ad + -6bc + 6bc + 12bd = 0 + 6bc Combine like terms: -6bc + 6bc = 0 15ac + -30ad + 0 + 12bd = 0 + 6bc 15ac + -30ad + 12bd = 0 + 6bc Remove the zero: 15ac + -30ad + 12bd = 6bc Add '-12bd' to each side of the equation. 15ac + -30ad + 12bd + -12bd = 6bc + -12bd Combine like terms: 12bd + -12bd = 0 15ac + -30ad + 0 = 6bc + -12bd 15ac + -30ad = 6bc + -12bd Reorder the terms: 15ac + -30ad + -6bc + 12bd = 6bc + -6bc + -12bd + 12bd Combine like terms: 6bc + -6bc = 0 15ac + -30ad + -6bc + 12bd = 0 + -12bd + 12bd 15ac + -30ad + -6bc + 12bd = -12bd + 12bd Combine like terms: -12bd + 12bd = 0 15ac + -30ad + -6bc + 12bd = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(5ac + -10ad + -2bc + 4bd) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(5ac + -10ad + -2bc + 4bd)' equal to zero and attempt to solve: Simplifying 5ac + -10ad + -2bc + 4bd = 0 Solving 5ac + -10ad + -2bc + 4bd = 0 Move all terms containing a to the left, all other terms to the right. Add '2bc' to each side of the equation. 5ac + -10ad + -2bc + 2bc + 4bd = 0 + 2bc Combine like terms: -2bc + 2bc = 0 5ac + -10ad + 0 + 4bd = 0 + 2bc 5ac + -10ad + 4bd = 0 + 2bc Remove the zero: 5ac + -10ad + 4bd = 2bc Add '-4bd' to each side of the equation. 5ac + -10ad + 4bd + -4bd = 2bc + -4bd Combine like terms: 4bd + -4bd = 0 5ac + -10ad + 0 = 2bc + -4bd 5ac + -10ad = 2bc + -4bd The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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